In this paper, we address the combined problem of assigning students to schools and generating school bus routes for special needs students. Special needs students typically require additional accommodations, both in terms of the services available at school and during pick-ups and drop-offs. This introduces additional complexities to the problems of assignment and routing for students. We develop a mathematical model that jointly addresses these problems, and incorporate multi-loads and heterogeneous bus fleet features. The model simultaneously assigns special needs students to schools based on their level of need and the availability of resources, and generates efficient routes to transport them to their designated schools. We propose a two-phase heuristic approach using the capacitated clustering problem, which is capable of generating high-quality solutions. We evaluate our proposed methodology using several randomly generated instances, and a real-world case study in Fort Smith, Arkansas. The results from the case study demonstrate that the proposed methodology can reduce the total miles traveled by buses by over 35% on average, when compared to previously developed heuristics in the literature for the same case study.

在本文中，我们解决了将学生分配到学校和为特殊需要的学生生成校车路线的综合问题。特殊需要的学生通常需要额外的住宿，无论是在学校提供的服务还是在接送服务期间。这给学生的分配和路由问题带来了额外的复杂性。我们开发了一个数学模型来共同解决这些问题，并结合了多负载和异构巴士车队的特点。该模型同时根据特殊需求学生的需求水平和资源可用性将他们分配到学校，并生成有效的路线将他们运送到指定的学校。我们提出了一种使用容量聚类问题的两阶段启发式方法，它能够生成高质量的解决方案。我们使用几个随机生成的实例和阿肯色州史密斯堡的真实案例研究来评估我们提出的方法。案例研究的结果表明，与先前在同一案例研究的文献中开发的启发式方法相比，所提出的方法可以将公交车行驶的总里程平均减少 35% 以上。